Answer:
The faster pipe will take 16 hours to fill the pond alone
Step-by-step explanation:
* Lets explain how to solve the problem
- A sewage treatment plant has two inlet pipes to its settling pond
- One pipe can fill the pond 3 times as fast as the other pipe
∴ The rate of the faster pipe is 3 times the rate of the second pipe
- The rate and the time are inverse proportion because;
time = job/rate and the job here is constant (fill pool), then
time × rate = constant
∵ The rate of the faster pipe is 3 times the rate of the second pipe
∴ The time of the second pipe is 3 times the time of the faster pipe
- Assume that the time of the faster pipe is t
∵ The time of the faster pipe is t
∴ The time of the second pipe is 3t
- Together they can fill the pond in 12 hours
∴ [tex]\frac{1}{3t}+\frac{1}{t}=\frac{1}{12}[/tex]
- The L.C.M of 3t and t is 3t
∴ [tex]\frac{1}{3t}+\frac{3}{3t}=\frac{1}{12}[/tex]
∴ [tex]\frac{1+3}{3t}=\frac{1}{12}[/tex]
∴ [tex]\frac{4}{3t}=\frac{1}{12}[/tex]
- By using cross multiplication
∴ 48 = 3t
- Divide both sides by 3
∴ t = 16
∵ t represents the time of the faster pipe
∴ The time of the first pipe is 16 hours
* The faster pipe will take 16 hours to fill the pond alone
